Joe Bob has a cousin Don who consumes goods 1 and 2.Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good 2.Which of the following utility functions is the only one that would not represent Don's preferences? A)U(x₁, x₂)=min{2x₁, 3x₂}. B)U(x₁, x₂)=20x₁ + 30x₂ + 10,000. C)U(x₁, x₂)=2x₁ + 3x₂ + 1000. D)U(x₁, x₂)=4x²₁ + 12x₁x₂ + 9x²₂. E)More than one of the above does not represent Don's preferences.

Question

Quizplus · Accepted Answer

In order for an utility function to represent Don's preferences, it must satisfy the condition that 3 units of good 1 is always a perfect substitute for 2 units of good 2. The only utility function that does not satisfy this condition is option A, where the marginal utility of good 1 is twice the marginal utility of good 2. This implies that Don would not be willing to substitute 3 units of good 1 for 2 units of good 2 at all levels of consumption, which contradicts his stated preference.

Joe Bob Has a Cousin Don Who Consumes Goods 1